{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "ResSimultn_HeatDiff_1D.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyMKxocRkFKfmBqjryM/9mC3",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Divyanshu-ISM/Oil-and-Gas-data-analysis/blob/master/ResSimultn_HeatDiff_1D.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k4rwtvz_z1Gl",
        "colab_type": "text"
      },
      "source": [
        "# Numerical simulation of heat equation in 1D \n",
        "\n",
        "Problem statement : T(w) = 40 C | T(e) = 20 C\n",
        "                  : Left to right heat flow with L lengthed rod and n nodes\n",
        "\n",
        "## The equation : \n",
        "### $ \\frac {\\partial T}{\\partial t} = \\alpha \\frac {\\partial^2 T}{\\partial x^2} $"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yxRf0VzlygT_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6b7PcuIn162w",
        "colab_type": "text"
      },
      "source": [
        "del2_T/del_x2 = (T(i+1) - 2T(i) + T(i-1)/(dx^2)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PCI8UOtV2ad9",
        "colab_type": "text"
      },
      "source": [
        "### Forward Euler's eqn:\n",
        "\n",
        "T (t+dt) = T(t) + ((dT/dt) @ t)* dt"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r7LkzM633nQe",
        "colab_type": "text"
      },
      "source": [
        "# Workflow - \n",
        "\n",
        "1. Start with an initial Temperature (vector) for all blocks. \n",
        "2. Find the temperature derivative for each block. \n",
        "3. Run a loop and hence find the new Temperature distribution for each block, for successive time intervals."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JCqCAGDmMBzn",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import pylab as pl\n",
        "from IPython import display\n",
        "import time"
      ],
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "W1LDDDQJy5io",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 921
        },
        "outputId": "14f25374-42e4-4b44-b2c0-bb01ad849bab"
      },
      "source": [
        "L = float(input('\\n Enter the Length of the rod in meters L=')) #L = 0.1 m\n",
        "\n",
        "n = int(input('\\n Enter the number of discrete blocks n='))    #n = 10\n",
        "\n",
        "alpha = 0.0001 #Thermal conductivity of steel\n",
        "\n",
        "#Surface temperatures \n",
        "T_w = 40 #degrees celcius\n",
        "T_e = 20 #degrees celcius\n",
        "\n",
        "#Initial Temperature condition- All blocks are cool and at zero deg. \n",
        "Ti = 0\n",
        "\n",
        "#Thickness/Length of each gridblock\n",
        "\n",
        "dx = L/n\n",
        "\n",
        "t_final = 60 #seconds \n",
        "\n",
        "dt = 0.01 #seconds\n",
        "\n",
        "x = np.linspace(dx/2 , L - dx/2 , n)  # 40C --> |  .  |  .  |  .  |  .  | <--20C\n",
        "\n",
        "T = np.ones(n)*Ti\n",
        "\n",
        "dTdt = np.empty(n)\n",
        "\n",
        "t = np.arange(0,t_final,dt)\n",
        "\n",
        "#Definition of terms Complete. Now time for computation in time.\n",
        "\n",
        "ax1 = plt.figure(figsize=(12,5))\n",
        "plt.grid()\n",
        "plt.style.use('fivethirtyeight')\n",
        "plt.title('Heat Diffusion Through a Rod - A simulation in time!')\n",
        "plt.axis([0,L,0,50])\n",
        "\n",
        "\n",
        "\n",
        "for j in range(1,len(t)):\n",
        "  plt.clf()\n",
        "  for i in range(1,n-1):\n",
        "    dTdt[i] = alpha*(T[i+1]-2*T[i]+ T[i-1])/(dx**2)\n",
        "    #But this is looping just over internal nodes\n",
        "  #For external nodes - 0 and n-1\n",
        "  dTdt[0] = alpha*(T[1]-2*T[0]+ T_w)/(dx**2)\n",
        "  dTdt[n-1] = alpha*(T_e-2*T[n-1]+ T[n-2])/(dx**2)\n",
        "  T = T + dTdt\n",
        "  # plt.figure(1)\n",
        "  plt.plot(x,T)\n",
        "  # plt.axis([0,L,0,50])\n",
        "  # plt.show()\n",
        " \n",
        "  plt.xlabel('Distance (x)')\n",
        "  plt.ylabel('Temperature C')\n",
        "  \n",
        "  display.clear_output(wait=True)\n",
        "  display.display(pl.gcf())\n",
        "  time.sleep(1.0)\n",
        "\n",
        "  # plt.show()\n",
        "  # plt.pause(0.0000000000000000001)\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "error",
          "ename": "KeyboardInterrupt",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-36-e277786846ec>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     57\u001b[0m   \u001b[0mdisplay\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclear_output\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mwait\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     58\u001b[0m   \u001b[0mdisplay\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdisplay\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgcf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 59\u001b[0;31m   \u001b[0mtime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msleep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1.0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     60\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     61\u001b[0m   \u001b[0;31m# plt.show()\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xVPW9oTRFDCV",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Dhx3w_UcK8oY",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}